The curve $C$ has equation $y=\frac{3{{x}^{2}}+9x+7}{x+2}$. By expressing the equation of $C$

Question

The curve $C$ has equation $y=\frac{3{{x}^{2}}+9x+7}{x+2}$. By expressing the equation of $C$ in the form $y=3x+a+\frac{b}{x+2}$, where $a$ and $b$ are non-zero constants, write down the equations of the asymptotes of $C$.[2] Describe a pair of transformations that will transform $C$ to the graph of $y=3x+\frac{1}{x}$.[2]

Accepted Answer

(i) $x=-2$ and $y=3x+3$ (ii) Translation of $2$ units in the positive $x$-direction, Translation of $3$ units in the positive $y$-direction. OR Translation of $3$ units in the positive $y$-direction, Translation of $2$ units in the positive $x$-direction.

2018 ACJC P1 Q9

2018 ACJC P1 Q9

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